| Acronym | ... |
| Name | 2srid (?) |
| Circumradius | sqrt[sqrt(5)+11/4] = 2.232951 |
| Vertex figure |
2[3,4,10/2,4] (type A) or 2[6/2,4,5,4] (type B) or 2[6/2,4,10/2,4] (type C) |
|
Snub derivation / VRML |
|
| General of army | srid |
| Colonel of regiment | srid |
| Confer |
|
Looks like a compound of 2 small rhombicosidodecahedra (srid), and indeed vertices, edges, and {4} coincide by pairs (type C). For type A additionally {3} resp. for type B additionally {5} coincide by pairs as well.
Incidence matrix according to Dynkin symbol
β3β5x (type A)
demi( . . . (a)) | 60 * | 1 2 0 1 | 1 0 1 2
demi( . . . (b)) | * 60 | 1 0 2 1 | 0 1 1 2
-----------------+-------+-------------+------------
both( . . x ) | 1 1 | 60 * * * | 0 0 1 1
sefa( s3s . (a)) | 2 0 | * 60 * * | 1 0 0 1
sefa( s3s . (b)) | 0 2 | * * 60 * | 0 1 0 1
sefa( . β5x ) | 1 1 | * * * 60 | 0 0 1 1
-----------------+-------+-------------+------------
s3s . (a) ♦ 3 0 | 0 3 0 0 | 20 * * *
s3s . (b) ♦ 0 3 | 0 0 3 0 | * 20 * *
. β5x ♦ 5 5 | 5 0 0 5 | * * 12 *
sefa( β3β5x ) | 2 2 | 1 1 1 1 | * * * 60
or
both( . . . ) | 120 | 1 2 1 | 1 1 2
--------------+-----+-----------+---------
both( . . x ) | 2 | 60 * * | 0 1 1
sefa( s3s . ) | 2 | * 120 * | 1 0 1
sefa( . β5x ) | 2 | * * 60 | 0 1 1
--------------+-----+-----------+---------
both( s3s . ) ♦ 3 | 0 3 0 | 40 * *
. β5x ♦ 10 | 5 0 5 | * 12 *
sefa( β3β5x ) | 4 | 1 2 1 | * * 60
starting figure: x3x5x
β5β3x (type B)
demi( . . . (a)) | 60 * | 1 2 0 1 | 1 0 1 2
demi( . . . (b)) | * 60 | 1 0 2 1 | 0 1 1 2
-----------------+-------+-------------+------------
both( . . x ) | 1 1 | 60 * * * | 0 0 1 1
sefa( s5s . (a)) | 2 0 | * 60 * * | 1 0 0 1
sefa( s5s . (b)) | 0 2 | * * 60 * | 0 1 0 1
sefa( . β3x ) | 1 1 | * * * 60 | 0 0 1 1
-----------------+-------+-------------+------------
s5s . (a) ♦ 5 0 | 0 5 0 0 | 12 * * *
s5s . (b) ♦ 0 5 | 0 0 5 0 | * 12 * *
. β3x ♦ 3 3 | 3 0 0 3 | * * 20 *
sefa( β5β3x ) | 2 2 | 1 1 1 1 | * * * 60
or
both( . . . ) | 120 | 1 2 1 | 1 1 2
--------------+-----+-----------+---------
both( . . x ) | 2 | 60 * * | 0 1 1
sefa( s5s . ) | 2 | * 120 * | 1 0 1
sefa( . β3x ) | 2 | * * 60 | 0 1 1
--------------+-----+-----------+---------
both( s5s . ) ♦ 5 | 0 5 0 | 24 * *
. β3x ♦ 6 | 3 0 3 | * 20 *
sefa( β5β3x ) | 4 | 1 2 1 | * * 60
starting figure: x5x3x
x3β5x (type C)
both( . . . ) | 120 | 1 1 1 1 | 1 1 1 1
--------------+-----+-------------+------------
both( x . . ) | 2 | 60 * * * | 1 0 1 0
both( . . x ) | 2 | * 60 * * | 0 1 1 0
sefa( x3β . ) | 2 | * * 60 * | 1 0 0 1
sefa( . β5x ) | 2 | * * * 60 | 0 1 0 1
--------------+-----+-------------+------------
x3β . ♦ 6 | 3 0 3 0 | 20 * * *
. β5x ♦ 10 | 0 5 0 5 | * 12 * *
both( x . x ) | 4 | 2 2 0 0 | * * 30 *
sefa( x3β5x ) | 4 | 0 0 2 2 | * * * 30
starting figure: x3x5x
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